Nicola Sturgeon has poured scorn on David Cameron’s EU deal, suggesting undecided voters will be disappointed with the lack of substance and that his demands for cuts to migrant benefits may have diminished the UK’s standing in the world.

Scotland’s first minister gave her verdict on the prime minister’s renegotiation as she warned him against making the case to remain in the EU a “miserable, negative, fear-based campaign” like the no camp’s strategy in the Scottish independence referendum.

She said she would fight “wholeheartedly” for a victory for the remain campaign, despite the prospect of a second independence poll if all the UK except Scotland votes to leave.

But she raised concerns that Cameron’s renegotiation efforts may have backfired and become a “danger” to the campaign to keep Britain in the EU because the reforms achieved will be underwhelming to undecided voters.

Asked for her thoughts on the deal, Sturgeon said: “I agree with the view it was something of a sideshow. But it could have been and could still be a dangerous sideshow. Nothing in the renegotiation – although that’s too grand a word for what actually happened – nothing was going to change my view as someone who wants to stay in Europe and nothing is going to change the views of an arch-Eurosceptic who wants out of Europe come what may.

“The danger is for those perhaps in the middle ground who are looking to that to try and make up their mind will inevitably be disappointed because it didn’t live up to what was promised. The danger of having a referendum so quickly after that is that it then occupies too big a place in the debate. But let’s hope none of that happens and it is a positive, upbeat, big-picture debate with the right outcomes.”

Sturgeon also suggested Cameron has given a negative impression of the UK by focusing on his demands to cut benefits for EU migrant workers at a time when the continent is struggling with the refugee crisis.

“The heads of government and heads of state were discussing the refugee crisis and instead spent time negotiating the taper rate at which the UK is allowed to cut benefits for EU workers. I can’t be the only person that wonders whether the UK’s standing in the world was being enhanced at that moment,” she said.

Sturgeon made the comments during a speech at St John’s church in Westminster hosted by the Resolution Foundation, in which she set out her hopes for a “thoroughly positive debate”.

She said: “One of the undoubted lessons of the Scottish experience is that a miserable, negative, fear-based campaign saw the no campaign in the Scottish referendum lose over the course of the campaign a 20-point lead.”

Sturgeon said there was no contradiction between believing in independence for Scotland while also supporting membership of the EU.

“If Scotland were to vote in favour of EU membership and the rest of the UK were to vote to leave – if Scotland, in other words, was to be outvoted – then there is a real chance that that could lead to a second referendum on Scottish independence,” she said.

But she added: “It’s not what I want to happen. Of course, I do want Scotland to be independent, but I don’t want Scotland to become independent because the UK chooses to leave the European Union. I want the UK as a whole to stay in the EU because I think that option will be better for the rest of the UK, I think it will be better for the EU and, should Scotland become independent in the future – something I believe will happen – I think it will be better for us, too.

“Ireland’s stance on the UK referendum is good evidence of this. Why wouldn’t we want our closest neighbour also to be a member of the European Union?”

The first minister is not the first advocate for the remain camp to have attacked Cameron’s EU deal as insubstantial.

The Labour leader, Jeremy Corbyn, has attacked the prime minister’s emergency brake on migrant benefits as ineffectual, as he branded the whole renegotiation a “theatrical sideshow”.